Trig Identities Help!

cotx-1 cosx-sinx
_____ = -------------------
cotx+1 cosx+sinx

please show all steps! thanks you!

knowing that cot(x) = cos(x)/sin(x), and that 1 = sin(x)/sin(x)

[cot(x) - 1]/[cot(x) + 1]
= {[cos(x)/sin(x)] - 1}/{[cos(x)/sin(x)] + 1}
= {[cos(x)/sin(x)] - [sin(x)/sin(x)]}/{[cos(x)/sin(x)] + [sin(x)/sin(x)]}
= {[cos(x) - sin(x)]/sin(x)}/{[cos(x) + sin(x)]/sin(x)}
= [cos(x) - sin(x)]/[cos(x) + sin(x)]

~
email me if you want a scan of this on paper, so it's easier to read overlord_of_all(at)yahoo.com